Easy -1.8 This is a straightforward application of basic polynomial differentiation requiring only recall of the power rule and simple substitution. It's a single-step C1 question with no problem-solving element, making it significantly easier than average A-level questions.
M1: \(x^n \rightarrow x^{n-1}\) including \(1 \rightarrow 0\); A1: Correct differentiation (Do not allow \(4x^0\) unless \(x^0 = 1\) is implied by later work)
M1: Substitutes \(x = 3\) into their \(\frac{dy}{dx}\) (not \(y\)). Substitutes \(x = 3\) into a "changed" function. They may even have integrated. A1: cao
Total: [4]
## Question 1:
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $y = x^3 + 4x + 1 \Rightarrow \frac{dy}{dx} = 3x^2 + 4(+0)$ | M1A1 | M1: $x^n \rightarrow x^{n-1}$ including $1 \rightarrow 0$; A1: Correct differentiation (Do not allow $4x^0$ unless $x^0 = 1$ is implied by later work) |
| Substitute $x = 3 \Rightarrow$ gradient $= 31$ | M1A1 | M1: Substitutes $x = 3$ into their $\frac{dy}{dx}$ (not $y$). Substitutes $x = 3$ into a "changed" function. They may even have integrated. A1: cao |
**Total: [4]**
Given $y = x ^ { 3 } + 4 x + 1$, find the value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ when $x = 3$\\
\hfill \mbox{\textit{Edexcel C1 2013 Q1 [4]}}